An express cargo train leaves Station A heading toward Station B at a constant speed of 50… — GMAT

An express cargo train leaves Station A heading toward Station B at a constant speed of $50$ miles per hour. At the exact same time, a local freight train leaves Station B heading toward Station A along a parallel track at a constant speed of $30$ miles per hour. If the total distance between Station A and Station B is $360$ miles, how many miles from Station A will the two trains meet?

Answer: 225 miles

Answer

The two trains will meet 225 miles from Station A.

When two objects move directly toward each other, their rate of approach is the sum of their speeds (

50 + 30 = 80

mph). Covering the total distance of

360

miles at a rate of

80

mph takes

4.5

hours. In

4.5

hours, the train traveling from Station A at

50

mph covers a distance of

50 \times 4.5 = 225

miles.

Step-by-Step Solution

Calculate the combined relative speed of both trains.

Relative speed =

50 + 30 = 80

miles per hour.

Since the two trains move toward each other, their relative rate of convergence is the sum of their individual speeds.

Calculate the time required for the two trains to meet.

Time

t = \frac{360 \text{ miles}}{80 \text{ mph}} = 4.5

hours.

Time equals total distance divided by combined relative speed.

Calculate the distance covered by the express train from Station A.

Distance =

50 \text{ mph} \times 4.5 \text{ hours} = 225

miles.

Distance equals the rate of the train departing Station A multiplied by the elapsed time.

Key Concept

Relative speed of converging objects moving toward each other

Estimated Time:1m 30s

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